Sparse Approximation by Matching Pursuit Using Shift-Invariant Dictionary

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10269)

Abstract

Sparse approximation of signals using often redundant and learned data dependent dictionaries has been successfully used in many applications in signal and image processing the last couple of decades. Finding the optimal sparse approximation is in general an NP complete problem and many suboptimal solutions have been proposed: greedy methods like Matching Pursuit (MP) and relaxation methods like Lasso. Algorithms developed for special dictionary structures can often greatly improve the speed, and sometimes the quality, of sparse approximation.

In this paper, we propose a new variant of MP using a Shift-Invariant Dictionary (SID) where the inherent dictionary structure is maximally exploited. The dictionary representation is simple, yet flexible, and equivalent to a general M channel synthesis FIR filter bank. Adapting the MP algorithm by using the SID structure gives a fast and compact sparse approximation algorithm with computational complexity of order \(\mathcal {O}(N \log N)\). In addition, a method to improve the sparse approximation using orthogonal matching pursuit, or any other block-based sparse approximation algorithm, is described. The SID-MP algorithm is tested by implementing it in a compact and fast C code (Matlab mex-file), and excellent performance of the algorithm is demonstrated.

Keywords

Sparse approximation Matching pursuit Dictionary Shift-invariant 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of StavangerStavangerNorway

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